Silicon carbide (SiC) detectors have excellent radiation detection capabilities for various radiation particles, including high energy resolution, fast response times, and good radiation resistance. A SiC radiation detection system was developed to measure the neutron fluence rate and the γ-ray dose rate in high intensity radiation fields. The system was composed of two SiC detectors, a temperature monitor, two preamplifiers for each SiC detector, a data acquisition unit with two signal channels, three pairs of communication devices, and an application software to analyze and visualize the measurement data. The two SiC detectors were fabricated based on two kinds of 4H-SiC diodes and used to respectively respond to neutrons and γ-rays. Repeated experiments showed that the two SiC detectors of the system can respond to α-particles, neutrons, and γ-rays. To verify the performance of the SiC detection system, including the response linearity of the neutron fluence rate, the measurement range of the γ-ray dose rate, and the radiation resistance of the SiC radiation detectors, the system was tested in multiple neutron and γ-ray fields. The tests results show the system can measure the neutron fluence rate from 5.64 × 10 2 cm−2 s−1 to 1.03 × 10 5 cm−2 s−1 with excellent linearity response, and the γ-ray dose rate from 0.005 Gy/h to 20 Gy/h. Furthermore, the SiC detectors demonstrated good radiation resistance. The neutron and γ-ray radiation field can still be measured stably by the system after exposure to neutron fluence of 1.07 × 10 14 cm−2 and γ-ray dose of 3.52 × 10 4 Gy. This work is the preliminary research to continue the exploration how to measure the n/γ hybrid fields accurately using SiC detectors considering the different energy of neutrons.